Plane On A Treadmill

Discussion in 'Et Cetera, Et Cetera' started by Dorset, Feb 21, 2007.

  1. Dorset

    Dorset New Member

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    I saw this on another forum and the response it got was unbelievable so I thought I'd try it out on you guys. (I found the answer that is accepted as correct by scientists which also happens to be the opposite of the conclusion that the forum that I got this question from came to).

    Lets see how bright you guys really are :wink:

    An Jet aircraft is on a runway that is also a conveyor belt. The conveyor exactly matches the aircrafts movement BUT is going in the opposite direction of the aircraft. Will the aircraft be able to get airborne?
     
  2. Gillette

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    Harrier?
     
  3. Dorset

    Dorset New Member

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    Lol, no, lets use a Boeing 747 for the question
     
  4. Shelby

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    Yeah, at least some of it when it blows the fuck up.
     
  5. DC_DEEP

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    With enough wind, yes. The speed of the wheels has nothing to do with it. Developing enough lift for take-off depends on relative windspeed. The combined velocity of the wings plus headwind has to be sufficient to create lift.

    In the average physics textbook, the student is usually asked to disregard some variables for some problems. In this case, if the only variables considered are the plane's forward momentum and the conveyor's backward momentum, no, the plane will not take off.
     
  6. Pecker

    Pecker Retired Moderator
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    No. It's Jet Blue.
     
  7. kamikazee_club

    kamikazee_club New Member

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  8. B_big dirigible

    B_big dirigible New Member

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    Heh heh, you got this from the Tractor Repair forum, didn't you? Those guys are lousy on some of the basics, like the only requirement for steady-state flight being that the lift+thrust vectors equal the weight+drag vectors.
     
  9. kamikazee_club

    kamikazee_club New Member

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    I just thought about it again for a sec and of course the only way for the aircraft to move forward is for wheel speed to exceed treadmill speed which in this example it cannot thus no forward motion thus no airflow thus no take off.
     
  10. DC_DEEP

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    The source of the thrust is irrelevant. Whether it comes from a power train to the wheels, or from a propeller, or from a jet engine, the lift is still not generated by the thrust; it is generated by wind flow over and around the wings. Windspeed is not a function of thrust applied, it is relative to the ambient wind velocity plus aircraft velocity. In my example, I was not suggesting that the thrust comes from the wheels. In the original post, it was stated that the runway is moving at an exact opposite vector as the thrust. The net effect would be zero forward velocity, and the net effect of that is no airflow over the foil (wings.) Without airflow over the wings, no lift is generated.

    Unless I am mistaken, simplistically stated: an aircraft wing is an airfoil, flat on the bottom and convex on the top. As air flows under the foil, the velocity of the airflow relative to the wings remains constant. As it travels over the convex upper surface of the wing, it has to move at a greater relative velocity, due to the greater surface area; the greater velocity induces lower pressure. Lower pressure above and higher pressure below creates the lift necessary for takeoff.

    Again, the source of the thrust is not relevant, and the wheels are only relevant in that they reduce the coefficient of friction between the aircraft and the runway; with a fixed runway, the thrust makes the aircraft move forward, creating an airflow over the fixed wings, creating the lift. With the runway moving at the same speed in the opposite direction, the net movement of the fuselage in a forward direction is negated, no airflow over the wings, no lift.
     
  11. Shelby

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    Exactly. And while I don't know this for sure, I was guessing that without the cooling effect of the wind the damn thing might overheat and explode.

    Hence my previous answer.
     
  12. JustAsking

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    DC and the other are totally right (IMHO as a physicist). Getting the plane off the ground has nothing to do with its ground speed. It has everything to do with its speed relative to the air.

    The power from the thrust of the engines is mostly consumed in overcoming the inertia of the plane (starting from standstill) and the drag from moving the plane through the air (even when it is on the ground). The actual rolling resistance soon becomes a small factor. Notice how those little carts can easily pull a big plane around on the ground.

    Suppose you start the engines and bring up the throttles, simultaneously you start the belt moving backwards, speeding the belt up to try to counteract the engine thrust and keep the plane from moving forward. You will quickly find that the belt will have to speed up incredibly fast in order to create enough backwards rolling friction to counteract the thrust of the engines.

    Since the plane is not yet moving forward in respect to the air, the wind resistance is close to zero. This means that all the power of the engines will go into simply rolling the plane forward on its wheels. In order to create enough backward rolling friction to keep it from moving forward, the belt will have to be moving a thousand miles per hour. The wheels will burn up before you get the belt moving fast enough.

    Take the case where the throttles are being slowly moved up towards full throttle and the belt is starting to move backwards faster and faster, but levels off at a belt speed of one hundred miles per hour and does not go any faster. I maintain that the plane will quickly start moving forward from that point and will end up in a mostly normal takeoff situation as if the belt were not moving at all.

    In this case, the plane starts building air speed (from its actual forward motion relative to the air, not the ground or the belt) the weight on the wheels will begin to decrease towards zero until the plane achieves enough lift for the wheels to completely off the belt, at which point the speed of the belt becomes completely immaterial.

    My conclusion: Short of the belt moving so fast backwards such that the wheels burn up, the belt will have very little influence on the plane taking off.
     
  13. B_big dirigible

    B_big dirigible New Member

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    The problem as posed says nothing about the wheel. The treadmill moves in one direction at exactly the same speed that the airplane moves in the other direction (as I interpret the wording). There's no requirement that the airplane even be touching the runway/conveyor for the postulated conditions to be met.

    DC_DEEP's summary of the physics is entirely sound. Airplanes fly by virtue of air speed, not ground speed.

    In real life, all tires have a maximum sustained speed rating, and if the plane rolled on the conveyor without taking off for an hour or so, the tires could conceivably overheat and consequently fail. But that's not part of this particular problem.
     
  14. JustAsking

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    If Emily Lotilla were still doing OpEd for Weekend Update, I can hear her asking, "Now whats all this fuss about 'Steaks on a Plane'?"
     
  15. socoken

    socoken New Member

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    So, if the belt matches the aircrafts "movement", meaning the jet is moving, It should be able to take off. The jet might be going 200mph forward, while the belt is going 200mph backwards. Sure, the wheels might be doing 400mph, but I would think that they would be rated to take that heat for a limited amount of time.

    Edit: BigD hit on this ahead of me, but I was taking my time in posting and never saw it.
     
  16. SpeedoGuy

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    Sorry, but if the plane's on a treadmill it gains no airspeed regardless of thrust applied. That's why joggers excercising on treadmills often use small table fans to cool themselves off and dry sweat: Because there's no airflow over their bodies.
     
  17. B_big dirigible

    B_big dirigible New Member

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    If the treadmill is moving backwards at speed V, the plane must be moving forwards at speed V. That was how the problem was stated. When the plane V equals the takeoff speed, up she goes. What the treadmill is doing in the meantime doesn't enter into it.

    All this assumes that the air isn't doing anything energetic - i.e., no wind.
     
  18. LeeEJ

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    Glad to see that nobody got completely lost.

    All the wheels do is hold an aircraft off the ground.

    Apply this treadmill scenario to real life. Say that the weather at a particular runway is blowing a 100-mph wind down its length (crazy weather, sure!). For the sake of demonstration, this particular aircraft has a minimum takeoff speed of 100 mph.

    If it were to start down the runway in the same direction that the wind is blowing, it would have a tailwind of 100 mph at the start, and as its ground speed reached 100 mph, its airspeed would eventually become 0 mph. For it to reach its 100 mph airspeed required for takeoff, it would have to continue to accelerate until it's going another 100 mph faster, which would also require a ground speed of 200 mph.

    Turn the aircraft around so that it points into the wind, and it could very well take off at a ground speed of 0 (zero) mph. It would still require the engines to run to push it through the aerodynamic drag, though.

    One other variant:

    Instead of an airplane on a treadmill, picture a person on a treadmill holding a kite. The kite's "thrust" is coming from the string, which is held by the person running on the treadmill. The string is effectively "thrust" in the sense that it keeps the kite from getting blown away by aerodynamic drag.

    Crank up the treadmill to 10 mph -- which would be enough windspeed for many kites to fly -- and see what happens.

    I'll bet a billion dollars that the kite will just sit there on the floor.

    (now, to find a sucker that has a billion dollars to spare!)
     
  19. SpeedoGuy

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    I'll try this analogy:

    Picture a bicyclist pedaling furiously on a stationary roller trainer, a proxy for our hypothetical jet plane on a treadmill.

    http://www.branfordbike.com/images/trainer/roller4.jpg

    The bicycle's chain and wheels are turning exactly as quickly as the roller trainer's wheels, at whatever rpm that may be. The bicyclist certainly works up a good sweat and the wheels develop enough gyroscopic force to balance the bicycle upright. Yet no matter how fast the bicyclist pedals, there is not a breath of air going ever across his/her body absent any environmental wind. i.e. no air drag resistance because there's no air moving.

    An airplane can't fly if no air moves across its wings.
     
  20. JustAsking

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    SpeedoGuy,
    Your analogy breaks down because the plane is applying thrust against the air, not against the ground or the treadmill. Your analogy does have some use, though. Suppose there was a rider on a bicycle on a treadmill, and there was also a person standing on the ground next to the treadmill.

    The standing person's job is to push the bike forward and bring it up to his walking speed. With the rider just coasting, how much harder is it for the pusher guy to get the bike to walking speed in the case of the treadmill moving, vs the treadmill not moving. The answer is that the pusher guy will hardly notice the treadmill moving or not moving. Since the rolling friction of the bike on the treadmill is very small, the action of the treamill will pose very little additional resistance to the forward motion of the bike.

    Now the pusher person is analogous to the jet engine, which is also not applying its thrust to the wheels and the ground (or the belt). Just like the case of the bike on the treadmill and the pusher, the backwards motion of the treadmill beneath the plane will offer very little resistance to the forward motion of the plane in comparison to the very strong thrust of the engines.

    In either case, the vehicle will start moving forward at almost the same rate with the treadmill either running backwards or not running at all.
     
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